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Bayesianism and Non-Ergodicity in Economics

The atomic hypothesis which has worked so splendidly in Physics breaks down in Psychics. We are faced at every turn with the problems of Organic Unity, of Discreteness, of Discontinuity – the whole is not equal to the sum of the parts, comparisons of quantity fails us, small changes produce large effects, the assumptions of a uniform and homogeneous continuum are not satisfied. Thus the results of Mathematical Psychics turn out to be derivative, not fundamental, indexes, not measurements, first approximations at the best; and fallible indexes, dubious approximations at that, with much doubt added as to what, if anything, they are indexes or approximations of. — John Maynard Keynes

Follow up:

Bayesianism is rather irritating because it allows adherents to try to avoid the Post-Keynesian criticisms regarding the heterogeneous nature of historical date which leads to its non-ergodic nature and the consequent problems with fundamental uncertainty. Because the Post-Keynesian critiques are usually aimed at frequentist interpretations of probability they often appear to be superficially overcome when arguing with a Bayesian. This, however, is categorically not the case.

For the past few days I’ve been trying to find a rather “clean” simple critique of Bayesianism that could be applied from a Post-Keynesian perspective. Now I think that I have found such a critique.

A Bayesian named Andrew Gelman has written up a summary of the criticisms thrown by their detractors and asked his colleagues to respond. The most important criticism that Gelman raises from a Post-Keynesian perspective involves the selection of “priors”. In Bayesian statistics “priors” are prior statistical distributions.

Sticking to an example I’ve used before, let’s say that I am interested in the probability, P, that a woman will call me in the morning between the hours of 9am and 11am. Now, since I am beginning my experiment I have literally no idea what the probability that a woman will call me tomorrow as I have no experimental data. The somewhat arbitrary probability that I then cook up will be called my “prior”. Gelman, adopting the voice of a critic (i.e. me), puts this as such:

Where do prior distributions come from, anyway? I don’t trust them and I see no reason to recommend that other people do, just so that I can have the warm feeling of philosophical coherence. To put it another way, why should I believe your subjective prior? If I really believed it, then I could just feed you some data and ask you for your subjective posterior. That would save me a lot of effort! (p447)

Just to clarify a “posterior” is the probability that is assigned when evidence is inputted. Anyway, Gelman’s version of the criticism seems to me a rather weak version and not nearly what I will be saying when I move to a Post-Keynesian criticism of this method if it is to be applied in economics. But it elicited a fairly clear response from Joseph Kadane. He wrote:

Why should I believe your subjective prior?” I don’t think you should. It is my responsibility as an author to explain why I chose the likelihood and prior that I did. If you find my reasons compelling, you may decide that your prior and likelihood would be sufficiently close to mine that it is worth your while to read my papers. If not, perhaps not. (p455)

So what Kadane is saying is that, to go back to my example, when we assign the first prior probability as to whether a woman will call me tomorrow morning we should make an argument and if someone else doesn’t like this argument they should throw my paper in the bin. The prior assigned, however, will always be in some sense arbitrary in that it will not be formed, as a posterior would, on the basis of data.

Now, here’s where the Post-Keynesian critique comes in. In economics we deal with heterogeneous historical data that is non-ergodic. Another way of putting this is that such data is composed of complex and unique events. An interest rate hike in 1928 is very different from an interest rate hike in 1979. The future, you see, does not mirror the past when we are talking about historical time.

Let’s go back to our example. What a Post-Keynesian economist is interested in is whether a woman will call tomorrow morning, not the probability that a woman will call on any given morning. But, of course, all we can then do is posit an argument to form a prior and you can, as Hadane says, accept or reject it. Great. That is what Post-Keynesians do. They lay out an argument. And everything stands or falls on that alone.

For Post-Keynesians there is no interest in positing a prior and then waiting for data to update the argument because the argument, by design, only works once. Post-Keynesian arguments are, in a sense, disposable. They are thrown out as historical time unfolds and new ones are constructed. The only manner in which to do this is through induction and the application of a skill-set that one acquires through one’s career. This is also, by the way, how historians and others like lawyers work.

The idea that you can find one True model that you then update with posteriors over and over again is wrong simply because the nature of the data is non-ergodic. To exaggerate slightly, but not much, there is a new argument for every new dawn. It is by wrestling with the changing nature of the economy that we come to understand it. Any other method is doomed to failure.

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